A Semianalytic Method for the Solution of the Neutron Transport Equation in Plane and Spherical Geometries

The source-free monoenergetic transport equation can be written as where for plane and for spherical geometries, respectively; Ω is the direction of motion with θ as its angle to the axis, An analytic expression for ψ(Z, cosθ) of the form is considered where P_n(cosθ) is the Legendre polynomial of order n; are combinations of exponential functions for the plane case and Bessel functions in the spherical formulation. A simple algorithm is developed that enables solutions to be found for any N using a small computer program.